The invention relates to a process for the preparation of elastomeric molded parts having urethane or urethane and urea linkages which comprises reacting(a) an organic polyisocyanate,(b) a polyhydroxyl compound selected from the group consisting of(i) polyester polyols with molecular weights of 1000 to 3000 and hydroxyl numbers of 170 to 35 produced by polycondensation of organic dicarboxylic acids and a polyol mixture of at least 3 polyols;(ii) polyether polyols having terminal ester groups, molecular weights of 1000 to 8000 and hydroxyl numbers of 170 to 15; and(iii) mixtures thereof;(c) a chain extenderwherein components (a) through (c) are processed according to reaction injection molding techniques in open or closed molds.The reaction is preferably carried out as a one-shot process and may also be carried out in the presence of blowing agents (d), auxiliaries (e), and additives (e).The non-cellular and/or microcellular elastomeric molded parts produced according to the method of this invention are particularly well suited for use in the automobile industry, for example, as bumper covers and body parts such as fenders, spoilers, wheel well expansions as well as engineering housing parts and runners. The cellular foams are used, for example, as shoe soles, armrests, headrests, safety coverings in the passenger compartment in automobiles as well as motorcycle and bicycle seats, seat cushions and cover layers in composite foams.